Systems and methods for semi-supervised depth estimation according to an arbitrary camera

ABSTRACT

System, methods, and other embodiments described herein relate to semi-supervised training of a depth model using a neural camera model that is independent of a camera type. In one embodiment, a method includes acquiring training data including at least a pair of training images and depth data associated with the training images. The method includes training the depth model using the training data to generate a self-supervised loss from the pair of training images and a supervised loss from the depth data. Training the depth model includes learning the camera type by generating, using a ray surface model, a ray surface that approximates an image character of the training images as produced by a camera having the camera type. The method includes providing the depth model to infer depths from monocular images in a device.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of U.S. Provisional Application No. 62/871,108, filed on, Jul. 6, 2019, and U.S. Provisional Application No. 62/984,903, filed on, Mar. 4, 2020, which are herein incorporated by reference in their entirety.

TECHNICAL FIELD

The subject matter described herein relates, in general, to systems and methods for determining depths of a scene from a monocular image, and, more particularly, to using a neural camera model to enable depth and pose learning according to camera images from an arbitrary camera source and with supervision.

BACKGROUND

Various devices that operate autonomously or that provide information about a surrounding environment often use sensors that facilitate perceiving obstacles and additional aspects of the surrounding environment. As one example, a robotic device uses information from the sensors to develop awareness of the surrounding environment in order to navigate through the environment and avoid hazards. In particular, the robotic device uses the perceived information to determine a 3-D structure of the environment so that the device may distinguish between navigable regions and potential hazards. The ability to perceive distances using sensor data provides the robotic device with the ability to plan movements through the environment and generally improve situational awareness about the environment.

In one approach, the robotic device may employ monocular cameras to capture images of the surrounding environment; however, the captured images do not explicitly include depth information. Instead, the robotic device can implement processing routines that derive depth information from the monocular images. Approaches to deriving depth information from monocular images, however, generally rely on various assumptions that can limit the application of this approach. For example, learning-based depth and pose estimation algorithms generally focus on pinhole camera models, because of the ease of calibrating such models and the closed-form solutions for reconstruction and projection operations. Thus, sources of training data are limited to cameras of this limited set, thereby limiting the approach overall.

Moreover, leveraging monocular images alone to train a model to generate depth estimates can also suffer from difficulties such as learning accurate metric scale. On one hand, not using ground truth data for training alleviates the burden of directly collecting this information, which is advantageous; however, this also results in the loss of learning metrically accurate representations. Consequently, difficulties persist with applying self-supervised monocular depth estimation in a robust context.

SUMMARY

In one embodiment, example systems and methods relate to semi-supervised training of a depth model using a neural camera model that is independent of a camera type. As previously noted, deriving depth data from monocular images may encounter various difficulties due to limitations on the source of the camera images and/or limitations on the source training data. That is, because of various difficulties with modeling certain camera types (e.g., fisheye, catadioptric, etc.), self-supervised monocular depth estimation generally focuses on images from pinhole types of cameras while avoiding images from other types of cameras. However, this limitation compounds in that the trained models are then only useful with pinhole cameras, thereby limiting possible implementations with other camera types. Moreover, as further stated, the depth model also does not learn metric scale because of the reliance on pairs of monocular images without ground truth data, which facilitates training overall, but can impair the usability of the depth model.

Therefore, in one embodiment, a depth system is disclosed that improves the training of a depth model by implementing a hybrid approach (also referred to herein as a semi-supervised approach) of training. In particular, the depth system maintains a self-supervised structure while further leveraging ground truth data to include the benefits of a supervised approach. For example, by including at least supervision with sparse data of the depth model, the depth system improves the performance of the depth model and causes the depth model to be scale aware and learn metrically accurate depths. To avoid further complication from the need for extensive ground truth data, the depth system can implement the supervision in a form such that the training uses sparse ground truth data without the use of extensive labeled training data. Consequently, the training architecture still uses a self-supervised loss with images from a monocular video but improves the self-supervised process with an additional refinement that uses less complex and, thus, more easily acquired depth data to then improve the training process.

Furthermore, the depth system also avoids shortcomings of using a single camera model by implementing a non-parametric camera model within a training architecture to permit learning of arbitrary camera types within a self/semi-supervised context. By implementing the training architecture to account for any type of camera (e.g., catadioptric, fisheye, pinhole, etc.) as the source of images, the depth system improves the scalability of the depth model and associated pose model, which can now leverage data from multiple cameras of any sort. For example, different cameras have different advantages, such as fisheye cameras with a larger field of view increasing the area covered by the image, and catadioptric cameras that have 360-degree field coverage of the surroundings, which can be particularly useful for autonomous driving scenarios with the comprehensive information included therein. Thus, the depth system may then leverage information from a wider variety of sources to improve knowledge about the surroundings, and, in the context of an autonomous vehicle, improve navigation of the vehicle through the environment. In this way, the depth system applies a combined supervised and self-supervised approach to training a depth model for monocular depth estimation using an arbitrary camera.

In one embodiment, a depth system for semi-supervised training of a depth model using a neural camera model that is independent of a camera type is disclosed. The depth system includes one or more processors and a memory communicably coupled to the one or more processors. The memory stores a network module including instructions that, when executed by the one or more processors, cause the one or more processors to acquire training data including at least a pair of training images derived from a monocular video and depth data associated with at least one of the training images. The memory stores a training module including instructions that, when executed by the one or more processors, cause the one or more processors to train the depth model using the training data to generate a self-supervised loss from the pair of training images and a supervised loss from the depth data. The training module includes instructions to train the depth model including instructions to learn the camera type by generating, using a ray surface model, a ray surface that approximates an image character of the training images as produced by a camera having the camera type. The training module includes instructions to provide the depth model to infer depths from monocular images in a device.

In one embodiment, a non-transitory computer-readable medium is disclosed for semi-supervised training of a depth model using a neural camera model that is independent of a camera type and including instructions that when executed by one or more processors cause the one or more processors to perform various functions. The instructions include instructions to acquire training data including at least a pair of training images derived from a monocular video and depth data associated with at least one of the training images. The instructions include instructions to train the depth model using the training data to generate a self-supervised loss from the pair of training images and a supervised loss from the depth data. Training the depth model includes learning the camera type by generating, using a ray surface model, a ray surface that approximates an image character of the training images as produced by a camera having the camera type. The instructions include instructions to provide the depth model to infer depths from monocular images in a device.

In one embodiment, a method for semi-supervised training of a depth model using a neural camera model that is independent of a camera type is disclosed. The method includes acquiring training data including at least a pair of training images derived from a monocular video and depth data associated with at least one of the training images. The method includes training the depth model using the training data to generate a self-supervised loss from the pair of training images and a supervised loss from the depth data. Training the depth model includes learning the camera type by generating, using a ray surface model, a ray surface that approximates an image character of the training images as produced by a camera having the camera type. The method includes providing the depth model to infer depths from monocular images in a device.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate various systems, methods, and other embodiments of the disclosure. It will be appreciated that the illustrated element boundaries (e.g., boxes, groups of boxes, or other shapes) in the figures represent one embodiment of the boundaries. In some embodiments, one element may be designed as multiple elements or multiple elements may be designed as one element. In some embodiments, an element shown as an internal component of another element may be implemented as an external component and vice versa. Furthermore, elements may not be drawn to scale.

FIG. 1 illustrates one embodiment of a vehicle within which systems and methods disclosed herein may be implemented.

FIG. 2 illustrates one embodiment of a depth system that is associated with training a depth model for monocular depth estimation within a semi-supervised context using an arbitrary camera model.

FIGS. 3A-3C illustrate different examples of depth data.

FIG. 4 illustrates a diagram of one embodiment of a training architecture.

FIG. 5A illustrates a diagram of one embodiment of a depth model

FIG. 5B illustrates a diagram of one embodiment of a ray surface model.

FIG. 6 illustrates one embodiment of a pose model.

FIG. 7 illustrates separate diagrams depicting differences between a pinhole camera model and a model for a camera having an arbitrary type.

FIG. 8 illustrates a flowchart of one embodiment of a method associated with semi-supervised training of a depth model using an arbitrary camera model.

DETAILED DESCRIPTION

Systems, methods, and other embodiments associated with semi-supervised training of a depth model using a neural camera model that is independent of a camera type are disclosed. As previously noted, deriving depth data from monocular images may encounter various difficulties in relation to the source of the training data. That is, when the training data originates from a video and takes the form of pairs of monocular images without ground truth data, the depth model does not have a basis from which to learn metric scale. Additionally, the training data is also generally from a single type of camera (e.g., pinhole). Thus, because various camera types (e.g., fisheye, catadioptric, etc.) can be difficult to accurately model, monocular depth estimation may generally focus on images from pinhole types of cameras while avoiding images from other types of cameras. However, training a depth model for a pinhole camera results in the depth model finding uses in instances where a pinhole camera is desirable, thereby limiting possible implementations with other camera types.

Therefore, in one embodiment, a depth system is disclosed that improves the training of a depth model by implementing a semi-supervised training architecture leveraging a non-parametric camera model to permit learning of arbitrary camera types for monocular depth estimation with the use of sparse ground truth data. By implementing the training architecture to be independent of a camera type and to supervise the depth maps, the depth system improves the scalability of the depth model and associated pose model while also learning metrically accurate depths. Thus, the depth system may leverage information from a wider variety of sources and without specific manual calibration or another tuning of the training architecture.

In regards to the supervision of training that forms the semi-supervised training process, whereas various approaches to supervised training of a depth model may use comprehensive depth maps (e.g., nearly per-pixel annotations) that correlate with images, the depth system implements the training architecture to use sparse depth data as ground truth information thereby using depth labels from, for example, less expensive LiDAR or other depth sensors. Thus, the depth system improves the training process by supplementing the self-supervised training with the ground truth data. That is, because annotated training data can be expensive to produce due to the use of expensive sensors (e.g., 64 beam LiDAR devices), and/or manual labeling processes, and because monocular video alone under a self-supervised process may result in scale ambiguities in the understanding of the trained depth model, the present systems and methods overcome the noted difficulties by using sparse depth data to supervise the self-supervised training without reliance on more comprehensive depth data from robust depth sensors.

Moreover, to achieve improvements in regards to using various camera types as the source of the monocular images, the depth system implements the training architecture to simultaneously learn a neural camera model associated with source images along with training the depth model and the pose model. As noted, the training integrates ground truth depth data, which may take the form of sparse LiDAR data that corresponds with at least a portion of the training images, by using both supervised and self-supervised losses to update the models. Accordingly, in one or more approaches, the depth system implements a neural camera model that is embodied by at least a ray surface model that accepts a monocular image as an input and produces a ray surface as an output that approximates an image character of the image. The depth system further provides the same monocular image to the depth model while providing an additional training image along with the original image to the pose model.

While the depth model produces depth estimates (i.e., a depth map) for pixels in the image, the ray surface model generates the ray surface. The ray surface associates pixels within the monocular image with directions in an environment from which light that generates the pixels in the camera originates. As one example, in the instance of a fisheye camera, the ray surface generally approximates a strong hemispherical distortion around the edges of the image that corresponds with such a camera type by defining rays or vectors pointing in a general direction of the locations in the environment.

In any case, the ray surface model functions to provide a ray surface as, in one embodiment, an approximation of the image character of the monocular image. That is, the ray surface is, in general, an approximation of how the camera manipulates light relative to actual locations in the environment to form the images. Thus, the ray surface model is broadly functioning to learn aspects associated with the source camera, which, when combined with ground truth depth data, allows the ray surface model to learn a camera center point. Accordingly, the depth system may use the ray surface to synthesize an image in combination with a depth map from the depth model and a transform from the pose model.

The depth system implements the neural camera model to facilitate synthesizing the image independent of prior knowledge of the source camera. The depth system then uses the synthesized image as an input to a self-supervised loss function that provides a loss value in relation to the original image. As an additional aspect, the depth system uses the sparse ground truth data as an input to a supervised loss function in combination with a generated depth map. From the supervised loss function, the depth system can generate the supervised loss. While the supervised loss and the self-supervised loss are discussed as part of a common training iteration, it should be appreciated that the semi-supervised training may include pre-training the depth model according to a self-supervised training process and subsequently further training the depth model using the supervised and self-supervised losses to further refine the model. In this way, the depth system applies a semi-supervised approach to training the models for monocular depth estimation using a camera model that is independent of the image source.

Referring to FIG. 1, an example of a vehicle 100 is illustrated. As used herein, a “vehicle” is any form of powered transport. In one or more implementations, the vehicle 100 is an automobile. While arrangements will be described herein with respect to automobiles, it will be understood that embodiments are not limited to automobiles. In some implementations, the vehicle 100 may be any robotic device or form of powered transport that, for example, observes surroundings to provide determinations therefrom, and thus benefits from the functionality discussed herein. In yet further embodiments, the vehicle 100 may be a statically mounted device, an embedded device, or another device that uses monocular images to derive depth information about a scene instead of being a motive device.

In any case, the vehicle 100 also includes various elements. It will be understood that, in various embodiments, it may not be necessary for the vehicle 100 to have all of the elements shown in FIG. 1. The vehicle 100 can have any combination of the various elements shown in FIG. 1. Further, the vehicle 100 can have additional elements to those shown in FIG. 1. In some arrangements, the vehicle 100 may be implemented without one or more of the elements shown in FIG. 1. While the various elements are illustrated as being located within the vehicle 100, it will be understood that one or more of these elements can be located external to the vehicle 100. Further, the elements shown may be physically separated by large distances and provided as remote services (e.g., cloud-computing services, software-as-a-service (SaaS), etc.).

Some of the possible elements of the vehicle 100 are shown in FIG. 1 and will be described along with subsequent figures. However, a description of many of the elements in FIG. 1 will be provided after the discussion of FIGS. 2-8 for purposes of the brevity of this description. Additionally, it will be appreciated that for simplicity and clarity of illustration, where appropriate, reference numerals have been repeated among the different figures to indicate corresponding or analogous elements. In addition, the discussion outlines numerous specific details to provide a thorough understanding of the embodiments described herein. Those of skill in the art, however, will understand that the embodiments described herein may be practiced using various combinations of these elements.

In any case, the vehicle 100 includes a depth system 170 that functions to train a depth model via a semi-supervised training process and provide depth estimates for an environment using the depth model. Moreover, while depicted as a standalone component, in one or more embodiments, the depth system 170 is integrated with the autonomous driving module 160, the camera 126, or another component of the vehicle 100. Additionally, as noted previously, one or more components of the depth system 170 may be cloud-based elements that are remote from the vehicle 100. The noted functions and methods will become more apparent with a further discussion of the figures.

With reference to FIG. 2, one embodiment of the depth system 170 is further illustrated. The depth system 170 is shown as including a processor 110. Accordingly, the processor 110 may be a part of the depth system 170, or the depth system 170 may access the processor 110 through a data bus or another communication path. In one or more embodiments, the processor 110 is an application-specific integrated circuit (ASIC) that is configured to implement functions associated with a network module 220 and a training module 230. In general, the processor 110 is an electronic processor, such as a microprocessor that is capable of performing various functions as described herein. In one embodiment, the depth system 170 includes a memory 210 that stores the network module 220 and the training module 230. The memory 210 is a random-access memory (RAM), read-only memory (ROM), a hard disk drive, a flash memory, or other suitable memory for storing the modules 220 and 230. The modules 220 and 230 are, for example, computer-readable instructions that, when executed by the processor 110, cause the processor 110 to perform the various functions disclosed herein.

Furthermore, in one embodiment, the depth system 170 includes a data store 240. The data store 240 is, in one embodiment, an electronic data structure stored in the memory 210 or another data store, and that is configured with routines that can be executed by the processor 110 for analyzing stored data, providing stored data, organizing stored data, and so on. Thus, in one embodiment, the data store 240 stores data used by the modules 220 and 230 in executing various functions. For example, as depicted in FIG. 2, the data store 240 includes training data 250, a depth model 260, a ray surface model 270, and a pose model 280 along with, for example, other information that is used and/or produced by the modules 220 and 230, such as depth map 290.

The training data 250 includes, for example, monocular images from the camera 126 or another imaging device. The monocular images are generally derived from one or more monocular videos that are comprised of a plurality of frames. As described herein, monocular images that comprise the monocular images are, for example, images from the camera 126 or another imaging device that is part of a video, and that encompasses a field-of-view (FOV) about the vehicle 100 of at least a portion of the surrounding environment. That is, the monocular image is, in one approach, generally limited to a subregion of the surrounding environment. As such, the image may be of a forward-facing (i.e., the direction of travel) 60, 90, 120-degree FOV, a rear/side facing FOV, or some other subregion as defined by the imaging characteristics (e.g., lens distortion, FOV, etc.) of the camera 126. In various aspects, the camera 126 is a pinhole camera, a fisheye camera, a catadioptric camera, or another form of camera that acquires images without a specific depth modality.

An individual monocular image itself includes visual data of the FOV that is encoded according to an imaging standard (e.g., codec) associated with the camera 126 or another imaging device that is the source. In general, characteristics of a source camera (e.g., camera 126) and the video standard define a format of the monocular image. Thus, while the particular characteristics can vary according to different implementations, in general, the image has a defined resolution (i.e., height and width in pixels) and format. Thus, for example, the monocular image is generally an RGB visible light image. In further aspects, the monocular image can be an infrared image associated with a corresponding infrared camera, a black/white image, or another suitable format as may be desired. Whichever format that the depth system 170 implements, the image is a monocular image in that there is no explicit additional modality indicating depth nor any explicit corresponding image from another camera from which the depth can be derived (i.e., no stereo camera pair). In contrast to a stereo image that may integrate left and right images from separate cameras mounted side-by-side to provide an additional depth channel, the monocular image does not include explicit depth information, such as disparity maps derived from comparing the stereo images pixel-by-pixel. Instead, the monocular image implicitly provides depth information in the relationships of perspective and size of elements depicted therein from which the depth model 260 derives the depth map/estimates.

Moreover, monocular video(s) from which the monocular images are derived may include observations of many different scenes. That is, as the camera 126 or another original source camera of the video progresses through an environment, perspectives of objects and features in the environment change, and the depicted objects/features themselves also change, thereby depicting separate scenes (i.e., particular combinations of objects/features). Thus, the depth system 170 may extract particular training pairs of monocular images from the monocular video for training. In particular, the depth system 170 generates the pairs from the video so that the pairs of images are of the same scene. As should be appreciated, the video includes a series of monocular images that are taken in succession according to a configuration of the camera. Thus, the camera may generate the images (also referred to herein as frames) of the video at regular intervals, such as every 0.033 s. That is, a shutter of the camera operates at a particular rate (i.e., frames-per-second (fps) configuration), which may be, for example, 24 fps, 30 fps, 60 fps, etc.

For purposes of the present discussion, the fps is presumed to be 30 fps. However, it should be appreciated that the fps may vary according to a particular configuration. Moreover, the depth system 170 need not generate the pairs from successive ones (i.e., adjacent) of images in a video, but instead can generally pair separate images of the same scene that are not successive as training images. Thus, in one approach, the depth system 170 pairs every other image depending on the fps. In a further approach, the depth system pairs every fifth image as a training pair. The greater the timing difference in the video between the pairs, the more pronounced a difference in camera position; however, this may also result in fewer shared features/objects between the images. As such, as previously noted, the pairs of monocular images for training are of a same scene and are generally constrained, in one or more embodiments, to be within a defined number of frames (e.g., 5 or fewer) to ensure correspondence of an observed scene between a pair of the monocular images. In any case, the pairs of monocular images generally have attributes of being monocular images from a monocular video that are separated by some interval of time (e.g., 0.06 s) such that a perspective of the camera changes between the pair of training images as a result of motion of the camera through the environment while generating the video.

Additionally, the training data 250, in one or more embodiments, further includes depth data as ground truth information about a scene depicted by the associated monocular images. The depth data indicates distances from a camera that generated the monocular images to features in the surrounding environment. The depth data, in one or more approaches, is sparse or generally incomplete for a corresponding scene such that only sparsely distributed points within a scene are annotated by the depth data as opposed to a depth map (e.g., depth map 290) that generally provides comprehensive depths for each separate depicted pixel. Consider FIGS. 3A, 3B, and 3C, which depict separate examples of depth data for a common scene. FIG. 3A depicts a depth map 300 that includes a plurality of annotated points generally corresponding to an associated monocular image on a per-pixel basis. Thus, the depth map 300 includes about 18,288 separate annotated points.

By comparison, FIG. 3B is an exemplary 3D point cloud 310 that may be generated by a LiDAR device having 64 scanning beams. Thus, the point cloud 310 includes about 1,427 separate points. Even though the point cloud 310 includes substantially fewer points than the depth map 300, the depth data of FIG. 3B represents a significant cost to acquire over a monocular video on an image-by-image basis. These costs and other difficulties generally relate to an expense of a robust LiDAR sensor that includes 64 separate beams, difficulties in calibrating this type of LiDAR device with the monocular camera, storing large quantities of data associated with the point cloud 310 for each separate image, and so on. As an example of sparse depth data, FIG. 3C depicts a point cloud 320. In the example of point cloud 320, a LiDAR having 4 beams generates about 77 points that form the point cloud 320. Thus, in comparison to the point cloud 310, the point cloud 320 includes about 5% of the depth data as the point cloud 310, which is a substantial reduction in data. However, the sparse information provides for sufficient supervision to facilitate overcoming scale ambiguities within the depth model when used as an additional point of determining loss for training in combination with the noted self-supervision process.

As an additional comparison of the FIGS. 3A-3C, note that within FIGS. 3A and 3B, the depth data is sufficiently dense to convey details of existing features/objects such as vehicles, etc. However, within the point cloud 320 of FIG. 3C, the depth data is sparse or, stated otherwise, the depth data vaguely characterizes the corresponding scene according to distributed points across the scene that do not generally provide detail of specific features/objects depicted therein. Thus, this sparse depth data that is sporadically dispersed in a thin/scant manner across the scene may not provide enough data for some purposes, such as object classification, but does provide sufficient information to supervise training the depth model 260.

While the depth data is generally described as originating from a LiDAR, in further embodiments, the depth data may originate from a set of stereo cameras, radar, or another depth-related sensor that is calibrated with the monocular camera 126 generating the monocular video. Furthermore, the depth data itself generally includes depth/distance information relative to a point of origin such as the camera 126, and may also include coordinates (e.g., x, y within an image) corresponding with separate depth measurements.

Further detail about the depth system 170 of FIG. 2, including the depth model 260, the ray surface model 270, and the pose model 280, will be provided in relation to FIG. 4 and subsequent figures. Thus, with reference to FIG. 4, one embodiment of a training architecture 400 associated with the depth system 170 is shown. As illustrated in FIG. 4, the training architecture 400 includes the depth model 260, the ray surface model 270, and the pose model 280 as implemented via the depth system 170. A training image pair including monocular image 410 and 420 from the monocular images are provided as inputs to the separate components. For example, the monocular image 410 is provided to all of the noted components, while the monocular image 420 is provided to the pose model 280.

In any case, the network module 220 includes instructions to apply the depth model 260 to the image 410 in order to generate the depth map 430 (i.e., depth map 290). The depth model 260, as illustrated in detail in FIG. 4, identifies an exemplary flow of a processing channel formed by the depth model 260 for processing monocular images, such as the monocular images. It should be appreciated that the depth model 260 is generally a machine learning algorithm that may be broadly characterized as a convolutional neural network (CNN) or as an encoder/decoder architecture, including convolutional and deconvolutional components.

The monocular image 410 is provided as an input into the depth model 260. The depth model 260, in one embodiment, includes an encoder 500 that accepts the image 410 as an electronic input and processes the image 410 to extract depth features. It should be appreciated that while the depth model 260 is discussed as a separate, distinct component, in one or more approaches, the depth model 260 is integrated with the network module 220 and/or the training module 230. Thus, the modules 220/230 may implement various routines/functions of the model 260 while storing data values (e.g., weights) of the depth model 260.

In any case, the depth features are, in general, aspects of the image that are indicative of spatial information that is intrinsically encoded therein. One example of an architecture for the encoding layers that form the encoder 500 may include a series of layers that function to fold (i.e., adapt dimensions of the feature map to retain the features) encoded features into separate channels iteratively reducing spatial dimensions of the image 410 while packing additional channels with information about embedded states of the features. The addition of the extra channels avoids the lossy nature of the encoding process and facilitates the preservation of more information (e.g., feature details) about the original monocular image 410.

Accordingly, in at least one approach, the encoder 500 is comprised of multiple encoding layers formed from a combination of two-dimensional (2D) convolutional layers, packing blocks, and residual blocks. While the encoder 500 is presented as including the noted components, it should be appreciated that further embodiments may vary the particular form of the encoding layers (e.g., convolutional and pooling layers without packing layers), and thus the noted configuration is one example of how the depth system 170 may implement the depth model 260.

The separate encoding layers generate outputs in the form of encoded feature maps (also referred to as tensors), which the encoding layers provide to subsequent layers in the depth model 260, including specific layers of a decoder 510 via skip connections that may function to provide residual information between the encoder 500 and the decoder 510. Thus, the encoder 500 includes a variety of separate layers that operate on the monocular image 410, and subsequently on derived/intermediate feature maps that convert the visual information of the monocular image 410 into embedded state information in the form of encoded features of different channels. In any case, the output of the encoder 500 is, in one approach, a feature map having a particular dimension (e.g., 512×H/32×W/32) that is transformed in relation to the image 410 (e.g., 3×H×W).

With continued reference to FIG. 5A, the depth model 260 further includes the decoder 510. One example of how the decoder 510 functions includes unfolding (i.e., adapting dimensions of the tensor to extract the features) the previously encoded spatial information in order to derive the depth map 430 according to learned correlations associated with the encoded features. That is, the decoding layers generally function to up-sample, through sub-pixel convolutions and other mechanisms, the previously encoded features into the depth map 430. In one or more arrangements, the decoding layers comprise unpacking blocks, two-dimensional convolutional layers, and inverse depth layers that function as output layers for different scales. In further aspects, the decoder 510 may also receive inputs via guiding connections from another model, such as identification of different instances within the image 410 from a semantic segmentation model that further guides determinations of the depths. While the decoder 510 is presented as including the noted components, it should be appreciated that further arrangements may vary the particular form of the decoding layers (e.g., deconvolutional layers without unpacking layers), and thus the noted configuration is one example of how the depth system 170 may implement the decoder 510.

In any case, returning to FIGS. 2 and 4, the depth system 170, in one embodiment, employs the depth model 260 to produce the depth map 430, which, in one or more arrangements, may be provided as an inverse mapping having inverse values for the depth estimates. In general, however, the depth map 430 is a pixel-wise prediction of depths for the image 410. That is, the depth model 260 provides estimates of depths for different aspects depicted in the image 410. It should be appreciated that, in one embodiment, the network module 220 generally includes instructions that function to control the processor 110 to execute various actions to control the depth model 260 to produce the depth map 330. The network module 220, in one or more approaches, acquires the training data 250 including pairs of images (e.g., 410/420) by controlling the camera 126 to capture the training data 250 from a data bus, or electronic memory, or another available communication pathway. Thus, the monocular images may be actively acquired or may be predefined and stored in the data store 240. Similarly, the depth system 170 may acquire the depth data in parallel with the monocular images to provide corresponding sparse depth information for the images.

In addition to providing the image 410 to the depth model 260, the training module 230 also provides the image 410 to the pose model 280 along with a second image 420 of a training pair. As previously outlined, the training pair are images of a same scene derived from a monocular video but taken apart in time as the source camera moves through the environment so that the images 410/420 have slightly different perspectives of the same scene. The pose model 280 is, in one or more embodiments, a machine learning algorithm that generates a rigid-body transformation 440 according to the noted images. An additional diagram of the pose model 280 is illustrated in FIG. 6. As shown in FIG. 6, the pose model 280 is, for example, a convolutional neural network that is comprised of a series of convolutional and average pooling layers. In one embodiment, the pose model 280 is comprised of seven convolutional layers followed by a final one-by-one convolutional layer and a six-channel average pooling operation. Of course, the noted configuration is one example of how the pose model 280 may be implemented, and, in further approaches, the pose model 280 may include a different combination of layers. The input to the pose model 280 includes the image 410 (target image), and a context image 420 that may be concatenated together as a single input. The training module 230, in at least one approach, uses the transformation 440 in combination with the ray surface 450 and the depth map 430 to produce the synthesized image 460, as will be discussed in greater detail subsequently.

Accordingly, the network module 220 includes instructions to control the ray surface model 270 to generate the ray surface 450. The ray surface model 270 is, in one or more approaches, a machine learning algorithm. As further detailed in FIG. 5B, the ray surface model 270 includes an encoder/decoder architecture with an encoder 520 and a decoder 530. The configuration of the encoder 520, in one or more approaches, may be similar to the encoder 500 of the depth model 260. Thus, in one or more arrangements, instead of the depth model 260 and the ray surface model 270, including separate encoders 500 and 520, the model 260 and the ray surface model 270 may share a single encoder (e.g., encoder 500). In general, the encoder 520 includes encoding layers arranged in a series of layers that function to reduce spatial dimensions of the image 410 into representations about embedded states of features included in the image 410.

Accordingly, in at least one approach, the encoder 520 is comprised of multiple encoding layers formed from a combination of two-dimensional (2D) convolutional layers, packing blocks, residual blocks, pooling layers, and so on. While the encoder 520 is presented as including the noted components, it should be appreciated that further embodiments may vary the particular form of the encoding layers, and thus the noted configuration is one example of how the depth system 170 may implement the ray surface model 270.

The ray surface model 270 further includes the decoder 530. In one example, the decoder 530 includes decoding layers that generally function to up-sample, through sub-pixel convolutions and other mechanisms, the previously encoded features into the ray surface 450. In one or more arrangements, the decoding layers comprise two-dimensional deconvolutional layers and other components as implemented to generate the ray surface 450. In any case, the ray surface model 270 produces the ray surface 450 according to an input of the image 410 in order to approximate an image character of the image 410. For example, the image character of the image 410 generally relates to a type of the source camera (e.g., camera 126) and how the camera produces the image 410 and other images in the monocular images relative to a ground truth of the surrounding environment. That is, the image character relates to aspects of the camera 126, such as lens distortion, a configuration of the camera system itself (e.g., FOV, reflecting mirrors), and other aspects that influence how the image is formed.

In any case, the ray surface model 270 provides ray surface(s) 450 that correspond to the image character of a source camera. In one or more approaches, the ray surface 350 may be comprised of a learned residual ray surface {circumflex over (Q)}_(r) that is added to a fixed ray surface template Q₀ to form the ray surface 450 {circumflex over (Q)}. The depth system 170 may implement the ray surface template Q₀ along with the learned residual ray surface {circumflex over (Q)}_(r) in order to facilitate difficulties with accurately learning the ray surface {circumflex over (Q)}. That is, randomly initializing the ray surface {circumflex over (Q)} leads to greater difficulty in ultimately learning an accurate representation. As such, because the camera type may be known, the training module 230 may initialize the training by using the ray surface template Q₀ in combination with the learned residual ray surface {circumflex over (Q)}_(r) to inject geometric priors into the learning framework. If no information is available about the source camera, then the training module 230 may, in or more approaches, provide the ray surface template Q₀ according to a “dummy” template based on a pinhole camera by lifting a plane at a fixed distance and normalizing a surface of the plane. Whichever approach is undertaken, the training module 230 includes instructions to initialize training with the ray surface template Q₀ and gradually introduce the learned ray surface residual {circumflex over (Q)}_(r).

The training module 230 then uses the ray surface 450 {circumflex over (Q)} to synthesize the image 460. In one or more arrangements, the training module 230 includes instructions to lift pixels to produce three-dimensional points using the ray surface 450, the depth map 430, and a camera offset. In one approach, instead of using a camera offset, the ray surface learns a camera center point that is embodied within the ray surface 450. The training module 230 then projects the three-dimensional points onto a context image to synthesize the image 460. It should be appreciated that generating the ray surface 450, lifting the pixels, and projecting the points may be collectively referred to as the neural camera model herein. In any case, a further illustration of this process will now be made in relation to FIG. 7.

FIG. 7 illustrates two separate processes associated with synthesizing an image. Example 700 illustrates the general process of synthesizing an image in relation to a pinhole camera model. Example 710 illustrates this process in relation to the neural camera model as implemented by the depth system 170. Example 700 illustrates the difference between the pinhole model 700 and the neural camera model 710 and further illustrates the distinctions through the correlations between the notations. In any case, in FIG. 7 illustrates lifting ϕ(p, d)=P and projecting π(P)=p for a single pixel p_(j) considering target image I_(t) and context image I_(c). Additionally, in FIG. 7, straight arrows represent unitary ray surface vectors Q(p), which may not be drawn to scale to facilitate visualization. Additionally, as illustrated in FIG. 7, p₁ is associated to p_(j).

To further define the notation applied in relation to FIG. 7, each pixel p=[u, v]^(T), a camera offset/center point is represented by S(u, v) as a 3D point and a unitary ray surface vector Q(u, v)∈

³, with D(u, v) representing scene depth along a ray. Additionally, the camera is the same for all points S(u, v)=S, ∀(u, v). The present training architecture 400, as shown in FIG. 4 produces a ray surface estimate (i.e., ray surface 450), which is represented as f_(r)=I→Q according to the ray surface model 270 {circumflex over (Q)}=f_(r)(I). Accordingly, the training module 230, in one or more arrangements, implements the lifting operation according to equation (1). P(u,v)=S(u,v)+{circumflex over (D)}(u,v){circumflex over (Q)}(u,v)  (1)

As noted in equation (1), the training module 230 scales a predicted ray vector {circumflex over (Q)}(u, v) from the ray surface 450 by a predicted depth {circumflex over (D)}(u, v) from the depth map 430, and further offsets this value by a camera offset/center S(u, v), which is common to all the pixels. In one approach, the training module 230 assumes that the camera center coincidences with the origin of the reference coordinate system and, thus, sets S(u, v)=[0, 0, 0]^(T)∀ u, v ∈ I. In a further aspect, the ray surface model produces the ray surface 450 to account for the camera center point. In such a configuration, the ray surface model 270 is learning the camera center point as a function of including the ground truth depth data 470 as part of the semi-supervised training.

In any case, as a result of the lifting operation P_(t)={P_(j)}_(j=1) ^(HW) produces pixels from I_(t) as 3D points. To project the 3D points, the training module 230, in one approach, searches for each point P_(j) to find a corresponding pixel p_(i) ∈ I_(c) with ray surface vector {circumflex over (Q)}_(i)={circumflex over (Q)}_(c)(p_(i)) that most closely matches the direction of P_(j) to the camera center S_(c). This direction is indicated as r_(c→j)=P_(j)−S_(c). Thus, the training module 230 searches for p*_(i) such that: p _(i)*=arg max_(p) _(i) _(∈I) _(c)

{circumflex over (Q)} _(c)(p _(i)),r _(c→j)

  (2)

To resolve this point from equation (2), in one or more approaches, the training module 230 may further include instructions to implement the arg max function as a soft max function. For example, to project 3D points P_(t) onto context image I_(c), the training module 230 is to find for each P_(j) ∈ P_(t) a corresponding pixel p_(i) ∈ I_(c) with surface ray {circumflex over (Q)}_(i) closest to the direction r_(c→j)=P_(j)−S_(c). Accordingly, the training module 230 calculates, in one or more approaches, the dot product of each r_(c→j) with each ray vector {circumflex over (Q)}_(i) to obtain a (H×W)² tensor M with each coefficient M_(ij)=

{circumflex over (Q)}_(i), r_(c→j)

=M(p_(i), P_(j)) representing a similarity between {circumflex over (Q)}_(i) and r_(c→j). Accordingly, the neural camera model, as implemented via the training module 230 and the network module 220 provides for: i*=arg max_(i) M(p _(i) ,P _(j))  (3)

However, to further make the operation differentiable, the training module 230 implements a soft max determination in place of the arg max with temperature τ to obtain the following implementation:

$\begin{matrix} {{\overset{\sim}{M}\left( {p_{i},P_{j}} \right)} = \frac{\exp\left( {{M\left( {p_{i},P_{j}} \right)}/\tau} \right)}{\left( {\sum\limits_{i}{\exp\left( {{M\left( {p_{i},P_{j}} \right)}/\tau} \right)}} \right)}} & (4) \end{matrix}$

The training module 230 further anneals the temperature over a defined time so that the tensor becomes approximately one/hot for each pixel. The training module 230 may further acquire the 2D-3D association for projecting by multiplying with a vector of pixel indices. In this way, the training module 230 implements the projecting in a fully differentiable manner.

Furthermore, because rays at each pixel are independent and, thus, can point in any given direction, the training module 230 implements the searching for the point as part of the projecting operation, in one or more arrangements, using a patch-based search that avoids searching over the entire context image. That is, the training module 230 may restrict the search involved in projecting the 3D points to a small h×w grid in the context image I_(c) surrounding the (u, v) coordinates of the target pixel p_(t). The training module 230 is capable of limiting the search space to a patch/grid about the target pixel since, in general, the motion of the vehicle 100 or source camera is small enough to produce correct associations within the patch. In further aspects, the training module 230 may implement further aspects to reduce memory requirements and improve performance, such as performing the search at half resolution, and then up-sampling the results to produce a pixel-wise estimate via, for example, interpolation. Consequently, the depth system 170 is able to synthesize the image 460 independently of the camera type for the images of the training data 250.

Continuing with FIG. 4 and the training module 230, in one or more arrangements, the training module 230 then uses the synthesized image 460 to generate a self-supervised loss 480 according to a loss function. In one or more embodiments, the loss function generates the loss as an appearance-based loss, such as a photometric loss. Thus, as one example, the loss function may calculate the photometric loss at the pixel level according to a structural similarity (SSIM) that may be combined with an L1 loss term. The structural similarity component and the L1 loss both operate on comparisons between the original target image 410 and the synthesized image 460 that is a regenerated form of the original image 410 according to the process explained above.

In addition to using the synthesized image 460, the training module 230 may further generate an additional component of the loss using the depth map 430. In one approach, the additional component is a depth smoothness loss. The depth smoothness component generally functions to regularize the depth in textureless image regions by penalizing high depth gradients in areas of low color gradients. Furthermore, the training module 230, in at least one embodiment, implements a supervised loss function that may be independent or integrated as part of the self-supervised loss. In any case, the training module 230 determines the supervised loss by, for example, comparing the ground truth depth 470 with the depth map 430 (also referred to as depth map 290 herein). The particular supervised loss function implemented by the training module 230 for deriving the supervised loss may vary according to the implementation but generally compares the ground truth data 470 with corresponding points within the depth map 430 in order to compare the points with corresponding estimations and ground truths. In this way, the training module 230 can improve the self-supervised training process by integrating a semi-supervised element.

While the loss function is discussed as including the noted components, in further aspects, the training module 230 may implement the loss function with various combinations of the noted components or with additional components (e.g., a velocity loss, etc.). In any case, the training module 230 uses the loss value to train the depth model 260, the ray surface model 270, and the pose model 280 by backpropagating the loss value (e.g., supervised and self-supervised loss values) and updating parameters of the noted models. In this way, the depth system 170 implements a semi-supervised approach to monocular depth estimation that leverages a neural camera model to account for an arbitrary source of images as an input without explicit requirements for calibration and/or manual tuning according to the source camera and to also learn accurate metric scale.

As an additional point about the training of the depth model, while a single training stage is discussed, the depth system 170 may pre-train the models or use a multi-stage training process. For example, the depth system 170, in one approach, may initially train the models according to a wholly self-supervised approach. That is, the depth system 170 may initially train the models without the use of the ground truth depth data. Moreover, the depth system 170 may, in a further embodiment, train the depth model 260 using a pinhole camera model according to a purely self-supervised approach in order to initialize the depth model 260 and the pose model 280. In either approach, this first stage of training provides for initially learning depth by the depth model 260 but leaves the depth model 260 with intrinsic shortcomings, such as a lack of metric scale and learning of only the pinhole type of camera.

Consequently, the depth system 170 can follow this initial stage with training using the neural camera model and the ground truth depth data as supervision. Accordingly, the depth system 170 uses the depth model 260 and the pose model 280, but now also uses the ray surface model 270 and the ground truth depth data 470 to further train the depth model 260. In this way, the depth model 260 starts with prior knowledge to hasten the training the process but also learns a metrically accurate scale and further implements the neural camera model to learn different types of cameras.

Once trained, the depth system 170 provides the depth map 430 (290), in one or more approaches, to additional systems/modules in the vehicle 100 in order to control the operation of the modules and/or the vehicle 100 overall. In still further aspects, the network module 220 communicates the depth map 430 to a remote system (e.g., cloud-based system) as, for example, a mechanism for mapping the surrounding environment or for other purposes (e.g., traffic reporting, etc.). As one example, the network module 220 uses the depth map 430 to map locations of obstacles in the surrounding environment and plan a trajectory that safely navigates the obstacles. Thus, the network module 220, in one embodiment, uses the depth map 430, at least in part, to control the vehicle 100 to navigate through the surrounding environment.

In further aspects, the network module 220 conveys the depth map 430 to further internal systems/components of the vehicle 100, such as the autonomous driving module 160. By way of example, in one arrangement, the network module 220 acquires the depth map 430 and conveys the depth map 430 to the autonomous driving module 160 as an electronic input. In this way, the depth system 170 informs the autonomous driving module 160 of the depth estimates to improve situational awareness and planning of the module 160. As such, the module 160 may acquire the depth map 430 as a primary source of depth information for the surrounding environment or, in one approach, as a secondary source that verifies other means (e.g., LiDAR data). It should be appreciated that the autonomous driving module 160 is indicated as one example, and, in further arrangements, the network module 220 may provide the depth map 430 to the module 160 and other components in parallel.

Additional aspects of semi-supervised training of a depth model using monocular images according to a neural camera model will be discussed in relation to FIG. 8. FIG. 8 illustrates a flowchart of a method 800 that is associated with improving depth estimates for monocular images using a neural camera model that is independent of a camera type. Method 800 will be discussed from the perspective of the depth system 170 of FIGS. 1-2. While method 800 is discussed in combination with the depth system 170, it should be appreciated that the method 800 is not limited to being implemented within the depth system 170 but is instead one example of a system that may implement the method 800.

As an additional note about the general structure of the method 800, training the depth model 260 according to the semi-supervised training process is represented at blocks 820-850. It should be appreciated that training according to the noted approach generally occurs over multiple iterations prior to providing the depth model for use. In any case, once the depth model 260 is trained overall according to the semi-supervised process, the depth model 260 provides a metrically accurate mechanism for inferring depths from monocular images of a trained camera type, which the network module 220 may then provide to another device or use within the existing device to perceive information about an environment.

At 810, the training module 230 acquires the training data 250. In general, the training data 250 is comprised of pairs of training images and depth data. As previously identified, the depth data can be LiDAR data or depth data from another source. In any case, the depth data provides a mechanism by which the depth system 170 can supervise training of the depth model 260, the ray surface model 270, and the pose model 280. To supervise the training, the depth system 170 leverages the scattered depth data against a corresponding set of depth estimates in the depth map 290 that are generally less than a whole of the available depth estimates. That is, the depth system 170 effectively subsamples the depth estimate according to the depth data to provide supervision of a subset of the estimates.

Further, the pairs of monocular training images, as previously noted, include separate images from a monocular camera (e.g., camera 126) that form a video. Thus, an individual round of training for the depth model 260 includes two monocular images of a same scene from the video. The images may be consecutive but are generally separated by multiple intervening images in the video. This form of training that uses two separate monocular images is generally characterized as a self-supervised process that leverages a structure from motion (SfM) approach. In any case, the depth system 170 uses two images as input to the training architecture, and also adds the depth data as an additional supervised element to form the semi-supervised approach.

At 820, the network module 220 executes the depth model 260, the ray surface model 270 and the pose model 280 over the training data to produce the depth map 290, the transform, and the ray surface. The network module 220 executes the depth model 260 over one of the images (e.g., target image I_(t)) of the pair to generate a depth map 290 indicating depths associated with aspects represented in the image. Thus, after the network module 220 executes the depth model 260 to generate the depth map 290, the training module 230 may execute further training routines to advance the training process.

At 820, the network module 220 generates a ray surface using the ray surface model 270. As previously described, a ray surface approximates an image character of the monocular image provided as input. The image character generally describes the camera type from which the monocular image originates. Thus, the image character indicates at least aspects of the camera that influence how the image is generated, such as a format of the monocular image and lens distortion as produced by a camera having the camera type. Accordingly, the ray surface model 270 learns the camera type according to the image character to provide the ray surface.

The ray surface itself associates pixels within the monocular image with directions in an environment from which light that generates the pixels in the camera originate. In one or more approaches, the ray surface is comprised of a residual component and a fixed component. The ray surface model 270 learns the residual component by iteratively processing different images and updating through the disclosed training process, but the fixed component (also referred to as the template) is a geometric prior for the camera type.

At 820, the network module 230 generates the transform 440 using the pose model 280. As previously described, the transform describes a change in position of the source camera between frames (i.e., 410 and 420). The training module 230 uses the transform 440 when generating the synthesized image 360.

At 830, the training module 230 generates the self-supervised loss. In one or more approaches, generating the self-supervised loss includes creating the synthesized image 460 and using the synthesized image 460 to derive the self-supervised loss itself. In one or more approaches, the training module 230 synthesizes the image 460 from at least the ray surface (e.g., 450) and a depth map (e.g., 430) associated with the monocular image (i.e., 410). As implemented by the training module 230, creating the synthesized image 460 generally includes applying the neural camera model to the noted inputs to synthesize the image 460. The neural camera model implements various functions in combination with inputs, such as a lifting operation and a projection operation. The neural camera model functions to lift pixels from the depth map 430 to produce three-dimensional points using the ray surface and a camera offset or learned camera center point. Further, the neural camera model projects the three-dimensional points onto a context image to create the synthesized image. It should be appreciated that the neural camera model through the noted operations and by further implementing the ray surface model 270 to learn the ray surfaces that are associated with the source camera, permits the depth system 170 to train the depth model 260 and the pose model 280 independently of the source camera format/type.

The training module 230 then uses the derived information to calculate the self-supervised loss according to a self-supervised loss function. The loss characterizes an accuracy of the depth model 260 in producing the depth map 290. The self-supervised loss may take different forms, such as a photometric loss, a reprojection loss, a combination of different losses, and so on. In any case, the training module 230 synthesizes the image 460 from the depth map 330, and the transform 440 via a neural camera model (i.e., the ray surface 450 in combination with the lifting and projecting operations). The synthesized image 460 then functions as a basis for determining at least a portion of the self-supervised loss.

At 840, the training module 230 generates the supervised loss according to a supervised loss function. In one or more approaches, the training module 230 generates the supervised loss by comparing values between the depth map 290 and corresponding information from the depth data of the training data 250. As noted, the depth data may be sparse LiDAR data that permits the depth model 260 to learn metric scale by accounting for scale-aware differences between the depth map 290 and the sparse LiDAR data. In any case, the training module 230 may separately apply the supervised loss to the models 260, 270, and 280 or integrates the supervised loss with the self-supervised loss.

At 850, the training module 230 uses the supervised loss and the self-supervised loss to adapt the depth model 260. In one embodiment, adapting the depth model 260 generally involves changing weights within separate layers of the depth model 260. Thus, in at least one approach, the training module 230 changes weights to improve the generation of depth estimates for subsequent input images. Furthermore, the training module 230 may also train the pose model 280 and the ray surface model 270 using the same or similar losses. In this way, the depth system 170 implements a depth model to produce the depth estimates according to a semi-supervised approach that is based on a self-supervised structure from motion (SfM) process.

At 860, the training module 230 provides the depth model 260. The training module 230 may provide the depth model 260 to other systems and/or modules within the vehicle 100 or to other devices (e.g., other remote vehicles). In any case, the depth system 170 improves the depth model 260 through the noted approach of semi-supervised training by inducing metric scale into the depth model 260 while also training the depth model 260 on any camera type through the use of the neural camera model.

Additional aspects of synthesizing the image 460 according to a neural camera model as noted at block 830 will be further discussed subsequently. Initially, the neural camera model receives data inputs for synthesizing an image. As discussed previously, the neural camera model receives at least a ray surface, a depth map, and a transform (i.e., a rigid-body transformation) that are derived from a pair of training images. Next, the neural camera model scales predicted ray vectors from the ray surface using the depth map 290. Subsequently, the neural camera model adjusts the predicted ray vectors according to the camera offset or a learned camera center point(s). These functions generally form the lifting operation described previously.

After the lifting operation is complete, the training module 230 leverages the neural camera model to determine a patch-based data association for searching pixels in the synthetic image 460. In one approach, the neural camera model determines the associations by defining search grids for target pixels of the synthesized image 460 according to coordinates of respective ones of the target pixels and a defined grid size. Thus, the neural camera model determines a grid having dimensions height×width that is a space lesser than the whole image. In one approach, the grid may be 100×100 pixels or another suitable grid size. In any case, by using the grid to search the image, the neural camera model reduces the computational complexity of projecting the 3D points into pixels.

The neural camera model then applies a soft max approximation with an annealing temperature to search over the respective search grids. Applying a soft max approximation to derive each pixel in the synthesized image generally includes identifying a predicted ray vector from the ray surface that corresponds with a direction associated with each of the three-dimensional points as defined relative to the camera offset. In this way, the neural camera model can identify pixels of the synthesized image. The patch-based data association and the soft max determination generally form the projecting operation as previously described.

As a result of these operations, the neural camera model provides the synthesized image 460 as an output. Accordingly, integrating the neural camera model within a semi-supervised monocular depth estimation framework improves the training of the associated models by providing independence from the source camera such that the depth system 170 can operate on arbitrary cameras without a need to perform complex calibrations.

FIG. 1 will now be discussed in full detail as an example environment within which the system and methods disclosed herein may operate. In some instances, the vehicle 100 is configured to switch selectively between an autonomous mode, one or more semi-autonomous operational modes, and/or a manual mode. Such switching can be implemented in a suitable manner, now known or later developed. “Manual mode” means that all of or a majority of the navigation and/or maneuvering of the vehicle is performed according to inputs received from a user (e.g., human driver). In one or more arrangements, the vehicle 100 can be a conventional vehicle that is configured to operate in only a manual mode.

In one or more embodiments, the vehicle 100 is an autonomous vehicle. As used herein, “autonomous vehicle” refers to a vehicle that operates in an autonomous mode. “Autonomous mode” refers to navigating and/or maneuvering the vehicle 100 along a travel route using one or more computing systems to control the vehicle 100 with minimal or no input from a human driver. In one or more embodiments, the vehicle 100 is highly automated or completely automated. In one embodiment, the vehicle 100 is configured with one or more semi-autonomous operational modes in which one or more computing systems perform a portion of the navigation and/or maneuvering of the vehicle along a travel route, and a vehicle operator (i.e., driver) provides inputs to the vehicle to perform a portion of the navigation and/or maneuvering of the vehicle 100 along a travel route.

The vehicle 100 can include one or more processors 110. In one or more arrangements, the processor(s) 110 can be a main processor of the vehicle 100. For instance, the processor(s) 110 can be an electronic control unit (ECU). The vehicle 100 can include one or more data stores 115 for storing one or more types of data. The data store 115 can include volatile and/or non-volatile memory. Examples of suitable data stores 115 include RAM (Random Access Memory), flash memory, ROM (Read Only Memory), PROM (Programmable Read-Only Memory), EPROM (Erasable Programmable Read-Only Memory), EEPROM (Electrically Erasable Programmable Read-Only Memory), registers, magnetic disks, optical disks, hard drives, or any other suitable storage medium, or any combination thereof. The data store 115 can be a component of the processor(s) 110, or the data store 115 can be operatively connected to the processor(s) 110 for use thereby. The term “operatively connected,” as used throughout this description, can include direct or indirect connections, including connections without direct physical contact.

In one or more arrangements, the one or more data stores 115 can include map data 116. The map data 116 can include maps of one or more geographic areas. In some instances, the map data 116 can include information or data on roads, traffic control devices, road markings, structures, features, and/or landmarks in the one or more geographic areas. The map data 116 can be in any suitable form. In some instances, the map data 116 can include aerial views of an area. In some instances, the map data 116 can include ground views of an area, including 360-degree ground views. The map data 116 can include measurements, dimensions, distances, and/or information for one or more items included in the map data 116 and/or relative to other items included in the map data 116. The map data 116 can include a digital map with information about road geometry. The map data 116 can be high quality and/or highly detailed.

In one or more arrangements, the map data 116 can include one or more terrain maps 117. The terrain map(s) 117 can include information about the ground, terrain, roads, surfaces, and/or other features of one or more geographic areas. The terrain map(s) 117 can include elevation data in the one or more geographic areas. The map data 116 can be high quality and/or highly detailed. The terrain map(s) 117 can define one or more ground surfaces, which can include paved roads, unpaved roads, land, and other things that define a ground surface.

In one or more arrangements, the map data 116 can include one or more static obstacle maps 118. The static obstacle map(s) 118 can include information about one or more static obstacles located within one or more geographic areas. A “static obstacle” is a physical object whose position does not change or substantially change over a period of time and/or whose size does not change or substantially change over a period of time. Examples of static obstacles include trees, buildings, curbs, fences, railings, medians, utility poles, statues, monuments, signs, benches, furniture, mailboxes, large rocks, hills. The static obstacles can be objects that extend above ground level. The one or more static obstacles included in the static obstacle map(s) 118 can have location data, size data, dimension data, material data, and/or other data associated with it. The static obstacle map(s) 118 can include measurements, dimensions, distances, and/or information for one or more static obstacles. The static obstacle map(s) 118 can be high quality and/or highly detailed. The static obstacle map(s) 118 can be updated to reflect changes within a mapped area.

The one or more data stores 115 can include sensor data 119. In this context, “sensor data” means any information about the sensors that the vehicle 100 is equipped with, including the capabilities and other information about such sensors. As will be explained below, the vehicle 100 can include the sensor system 120. The sensor data 119 can relate to one or more sensors of the sensor system 120. As an example, in one or more arrangements, the sensor data 119 can include information on one or more LIDAR sensors 124 of the sensor system 120.

In some instances, at least a portion of the map data 116 and/or the sensor data 119 can be located in one or more data stores 115 located onboard the vehicle 100. Alternatively, or in addition, at least a portion of the map data 116 and/or the sensor data 119 can be located in one or more data stores 115 that are located remotely from the vehicle 100.

As noted above, the vehicle 100 can include the sensor system 120. The sensor system 120 can include one or more sensors. “Sensor” means any device, component and/or system that can detect, and/or sense something. The one or more sensors can be configured to detect, and/or sense in real-time. As used herein, the term “real-time” means a level of processing responsiveness that a user or system senses as sufficiently immediate for a particular process or determination to be made, or that enables the processor to keep up with some external process.

In arrangements in which the sensor system 120 includes a plurality of sensors, the sensors can work independently from each other. Alternatively, two or more of the sensors can work in combination with each other. In such a case, the two or more sensors can form a sensor network. The sensor system 120 and/or the one or more sensors can be operatively connected to the processor(s) 110, the data store(s) 115, and/or another element of the vehicle 100 (including any of the elements shown in FIG. 1). The sensor system 120 can acquire data of at least a portion of the external environment of the vehicle 100 (e.g., nearby vehicles).

The sensor system 120 can include any suitable type of sensor. Various examples of different types of sensors will be described herein. However, it will be understood that the embodiments are not limited to the particular sensors described. The sensor system 120 can include one or more vehicle sensors 121. The vehicle sensor(s) 121 can detect, determine, and/or sense information about the vehicle 100 itself. In one or more arrangements, the vehicle sensor(s) 121 can be configured to detect, and/or sense position and orientation changes of the vehicle 100, such as, for example, based on inertial acceleration. In one or more arrangements, the vehicle sensor(s) 121 can include one or more accelerometers, one or more gyroscopes, an inertial measurement unit (IMU), a dead-reckoning system, a global navigation satellite system (GNSS), a global positioning system (GPS), a navigation system 147, and/or other suitable sensors. The vehicle sensor(s) 121 can be configured to detect, and/or sense one or more characteristics of the vehicle 100. In one or more arrangements, the vehicle sensor(s) 121 can include a speedometer to determine a current speed of the vehicle 100.

Alternatively, or in addition, the sensor system 120 can include one or more environment sensors 122 configured to acquire, and/or sense driving environment data. “Driving environment data” includes data or information about the external environment in which an autonomous vehicle is located or one or more portions thereof. For example, the one or more environment sensors 122 can be configured to detect, quantify and/or sense obstacles in at least a portion of the external environment of the vehicle 100 and/or information/data about such obstacles. Such obstacles may be stationary objects and/or dynamic objects. The one or more environment sensors 122 can be configured to detect, measure, quantify and/or sense other things in the external environment of the vehicle 100, such as, for example, lane markers, signs, traffic lights, traffic signs, lane lines, crosswalks, curbs proximate the vehicle 100, off-road objects, etc.

Various examples of sensors of the sensor system 120 will be described herein. The example sensors may be part of the one or more environment sensors 122 and/or the one or more vehicle sensors 121. However, it will be understood that the embodiments are not limited to the particular sensors described.

As an example, in one or more arrangements, the sensor system 120 can include one or more radar sensors 123, one or more LIDAR sensors 124, one or more sonar sensors 125, and/or one or more cameras 126. In one or more arrangements, the one or more cameras 126 can be high dynamic range (HDR) cameras or infrared (IR) cameras.

The vehicle 100 can include an input system 130. An “input system” includes any device, component, system, element, or arrangement or groups thereof that enable information/data to be entered into a machine. The input system 130 can receive an input from a vehicle passenger (e.g., a driver or a passenger). The vehicle 100 can include an output system 135. An “output system” includes any device, component, or arrangement or groups thereof that enable information/data to be presented to a vehicle passenger (e.g., a person, a vehicle passenger, etc.).

The vehicle 100 can include one or more vehicle systems 140. Various examples of the one or more vehicle systems 140 are shown in FIG. 1. However, the vehicle 100 can include more, fewer, or different vehicle systems. It should be appreciated that although particular vehicle systems are separately defined, each or any of the systems or portions thereof may be otherwise combined or segregated via hardware and/or software within the vehicle 100. The vehicle 100 can include a propulsion system 141, a braking system 142, a steering system 143, throttle system 144, a transmission system 145, a signaling system 146, and/or a navigation system 147. Each of these systems can include one or more devices, components, and/or a combination thereof, now known or later developed.

The navigation system 147 can include one or more devices, applications, and/or combinations thereof, now known or later developed, configured to determine the geographic location of the vehicle 100 and/or to determine a travel route for the vehicle 100. The navigation system 147 can include one or more mapping applications to determine a travel route for the vehicle 100. The navigation system 147 can include a global positioning system, a local positioning system, or a geolocation system.

The processor(s) 110, the depth system 170, and/or the autonomous driving module(s) 160 can be operatively connected to communicate with the various vehicle systems 140 and/or individual components thereof. For example, returning to FIG. 1, the processor(s) 110 and/or the autonomous driving module(s) 160 can be in communication to send and/or receive information from the various vehicle systems 140 to control the movement, speed, maneuvering, heading, direction, etc. of the vehicle 100. The processor(s) 110, the depth system 170, and/or the autonomous driving module(s) 160 may control some or all of these vehicle systems 140 and, thus, may be partially or fully autonomous.

The processor(s) 110, the depth system 170, and/or the autonomous driving module(s) 160 can be operatively connected to communicate with the various vehicle systems 140 and/or individual components thereof. For example, returning to FIG. 1, the processor(s) 110, the depth system 170, and/or the autonomous driving module(s) 160 can be in communication to send and/or receive information from the various vehicle systems 140 to control the movement, speed, maneuvering, heading, direction, etc. of the vehicle 100. The processor(s) 110, the depth system 170, and/or the autonomous driving module(s) 160 may control some or all of these vehicle systems 140.

The processor(s) 110, the depth system 170, and/or the autonomous driving module(s) 160 may be operable to control the navigation and/or maneuvering of the vehicle 100 by controlling one or more of the vehicle systems 140 and/or components thereof. For instance, when operating in an autonomous mode, the processor(s) 110, the depth system 170, and/or the autonomous driving module(s) 160 can control the direction and/or speed of the vehicle 100. The processor(s) 110, the depth system 170, and/or the autonomous driving module(s) 160 can cause the vehicle 100 to accelerate (e.g., by increasing the supply of fuel provided to the engine), decelerate (e.g., by decreasing the supply of fuel to the engine and/or by applying brakes) and/or change direction (e.g., by turning the front two wheels). As used herein, “cause” or “causing” means to make, force, compel, direct, command, instruct, and/or enable an event or action to occur or at least be in a state where such event or action may occur, either in a direct or indirect manner.

The vehicle 100 can include one or more actuators 150. The actuators 150 can be any element or combination of elements operable to modify, adjust and/or alter one or more of the vehicle systems 140 or components thereof to responsive to receiving signals or other inputs from the processor(s) 110 and/or the autonomous driving module(s) 160. Any suitable actuator can be used. For instance, the one or more actuators 150 can include motors, pneumatic actuators, hydraulic pistons, relays, solenoids, and/or piezoelectric actuators, just to name a few possibilities.

The vehicle 100 can include one or more modules, at least some of which are described herein. The modules can be implemented as computer-readable program code that, when executed by a processor 110, implement one or more of the various processes described herein. One or more of the modules can be a component of the processor(s) 110, or one or more of the modules can be executed on and/or distributed among other processing systems to which the processor(s) 110 is operatively connected. The modules can include instructions (e.g., program logic) executable by one or more processor(s) 110. Alternatively, or in addition, one or more data store 115 may contain such instructions.

In one or more arrangements, one or more of the modules described herein can include artificial or computational intelligence elements, e.g., neural network, fuzzy logic or other machine learning algorithms. Further, in one or more arrangements, one or more of the modules can be distributed among a plurality of the modules described herein. In one or more arrangements, two or more of the modules described herein can be combined into a single module.

The vehicle 100 can include one or more autonomous driving modules 160. The autonomous driving module(s) 160 can be configured to receive data from the sensor system 120 and/or any other type of system capable of capturing information relating to the vehicle 100 and/or the external environment of the vehicle 100. In one or more arrangements, the autonomous driving module(s) 160 can use such data to generate one or more driving scene models. The autonomous driving module(s) 160 can determine position and velocity of the vehicle 100. The autonomous driving module(s) 160 can determine the location of obstacles, obstacles, or other environmental features including traffic signs, trees, shrubs, neighboring vehicles, pedestrians, etc.

The autonomous driving module(s) 160 can be configured to receive, and/or determine location information for obstacles within the external environment of the vehicle 100 for use by the processor(s) 110, and/or one or more of the modules described herein to estimate position and orientation of the vehicle 100, vehicle position in global coordinates based on signals from a plurality of satellites, or any other data and/or signals that could be used to determine the current state of the vehicle 100 or determine the position of the vehicle 100 with respect to its environment for use in either creating a map or determining the position of the vehicle 100 in respect to map data.

The autonomous driving module(s) 160 either independently or in combination with the depth system 170 can be configured to determine travel path(s), current autonomous driving maneuvers for the vehicle 100, future autonomous driving maneuvers and/or modifications to current autonomous driving maneuvers based on data acquired by the sensor system 120, driving scene models, and/or data from any other suitable source. “Driving maneuver” means one or more actions that affect the movement of a vehicle. Examples of driving maneuvers include: accelerating, decelerating, braking, turning, moving in a lateral direction of the vehicle 100, changing travel lanes, merging into a travel lane, and/or reversing, just to name a few possibilities. The autonomous driving module(s) 160 can be configured to implement determined driving maneuvers. The autonomous driving module(s) 160 can cause, directly or indirectly, such autonomous driving maneuvers to be implemented. As used herein, “cause” or “causing” means to make, command, instruct, and/or enable an event or action to occur or at least be in a state where such event or action may occur, either in a direct or indirect manner. The autonomous driving module(s) 160 can be configured to execute various vehicle functions and/or to transmit data to, receive data from, interact with, and/or control the vehicle 100 or one or more systems thereof (e.g., one or more of vehicle systems 140).

Detailed embodiments are disclosed herein. However, it is to be understood that the disclosed embodiments are intended only as examples. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the aspects herein in virtually any appropriately detailed structure. Further, the terms and phrases used herein are not intended to be limiting but rather to provide an understandable description of possible implementations. Various embodiments are shown in FIGS. 1-8, but the embodiments are not limited to the illustrated structure or application.

The flowcharts and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments. In this regard, each block in the flowcharts or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved.

The systems, components and/or processes described above can be realized in hardware or a combination of hardware and software and can be realized in a centralized fashion in one processing system or in a distributed fashion where different elements are spread across several interconnected processing systems. Any kind of processing system or another apparatus adapted for carrying out the methods described herein is suited. A typical combination of hardware and software can be a processing system with computer-usable program code that, when being loaded and executed, controls the processing system such that it carries out the methods described herein. The systems, components and/or processes also can be embedded in a computer-readable storage, such as a computer program product or other data programs storage device, readable by a machine, tangibly embodying a program of instructions executable by the machine to perform methods and processes described herein. These elements also can be embedded in an application product which comprises all the features enabling the implementation of the methods described herein and, which when loaded in a processing system, is able to carry out these methods.

Furthermore, arrangements described herein may take the form of a computer program product embodied in one or more computer-readable media having computer-readable program code embodied, e.g., stored, thereon. Any combination of one or more computer-readable media may be utilized. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. The phrase “computer-readable storage medium” means a non-transitory storage medium. A computer-readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium would include the following: a portable computer diskette, a hard disk drive (HDD), a solid-state drive (SSD), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a portable compact disc read-only memory (CD-ROM), a digital versatile disc (DVD), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer-readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.

Generally, module, as used herein, includes routines, programs, objects, components, data structures, and so on that perform particular tasks or implement particular data types. In further aspects, a memory generally stores the noted modules. The memory associated with a module may be a buffer or cache embedded within a processor, a RAM, a ROM, a flash memory, or another suitable electronic storage medium. In still further aspects, a module as envisioned by the present disclosure is implemented as an application-specific integrated circuit (ASIC), a hardware component of a system on a chip (SoC), as a programmable logic array (PLA), or as another suitable hardware component that is embedded with a defined configuration set (e.g., instructions) for performing the disclosed functions.

Program code embodied on a computer-readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber, cable, RF, etc., or any suitable combination of the foregoing. Computer program code for carrying out operations for aspects of the present arrangements may be written in any combination of one or more programming languages, including an object-oriented programming language such as Java™, Smalltalk, C++ or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a standalone software package, partly on the user's computer and partly on a remote computer, or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

The terms “a” and “an,” as used herein, are defined as one or more than one. The term “plurality,” as used herein, is defined as two or more than two. The term “another,” as used herein, is defined as at least a second or more. The terms “including” and/or “having,” as used herein, are defined as comprising (i.e., open language). The phrase “at least one of . . . and . . . ” as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items. As an example, the phrase “at least one of A, B, and C” includes A only, B only, C only, or any combination thereof (e.g., AB, AC, BC or ABC).

Aspects herein can be embodied in other forms without departing from the spirit or essential attributes thereof. Accordingly, reference should be made to the following claims, rather than to the foregoing specification, as indicating the scope hereof. 

What is claimed is:
 1. A depth system for semi-supervised training of a depth model using a neural camera model that is independent of a camera type, comprising: one or more processors; a memory communicably coupled to the one or more processors and storing: a network module including instructions that, when executed by the one or more processors, cause the one or more processors to acquire training data including at least a pair of training images derived from a monocular video and depth data associated with at least one of the training images; and a training module including instructions that, when executed by the one or more processors, cause the one or more processors to train the depth model using the training data to generate a self-supervised loss from the pair of training images and a supervised loss from the depth data, wherein the training module includes instructions to train the depth model including instructions to learn the camera type by generating, using a ray surface model that is a neural network, a ray surface that approximates an image character of the training images as produced by a camera having the camera type and to create a synthesized image according to at least the ray surface and a depth map by i) lifting pixels to produce three-dimensional points using the ray surface, the depth map, and a camera center point and ii) projecting the three-dimensional points onto a context image to create the synthesized image, and wherein the training module includes instructions to provide the depth model to infer depths from monocular images in a device.
 2. The depth system of claim 1, wherein the training module includes instructions to train the depth model including instructions to generate the supervised loss using a supervised loss function that compares values between the depth map and corresponding information from the depth data that is sparse Light Detection and Ranging (LiDAR) data, and wherein the training module includes instructions to generate the supervised loss using the sparse LiDAR data to train the depth model on metric scale by accounting for scale aware differences between the depth map and the sparse LiDAR data and learns a camera center point associated with the ray surface.
 3. The depth system of claim 1, wherein the training module includes instructions to lift the pixels including instructions to scale predicted ray vectors from the ray surface using the depth map and adjust the predicted ray vectors according to the camera center point, and wherein the training module includes instructions to project including instructions to apply a softmax approximation to derive each pixel in the synthesized image by identifying a predicted ray vector from the ray surface that corresponds with a direction associated with the three-dimensional points as defined relative to the camera center point.
 4. The depth system of claim 1, wherein the image character associated with the camera type includes at least a format of the monocular images and lens distortion, and wherein the ray surface associates pixels within the monocular images with directions in an environment from which light that generates the pixels in the camera originates.
 5. The depth system of claim 1, wherein the training module includes instructions to train the depth model to produce depth estimates according to a semi-supervised training process that integrates a self-supervised structure from motion (SfM) process, and wherein the training module includes instructions to train the depth model including instructions to use the self-supervised loss and the supervised loss to update at least the depth model, a pose model, and the ray surface model.
 6. The depth system of claim 1, wherein the self-supervised loss includes a photometric loss and a depth smoothness loss that separately account for pixel-level similarities, wherein the training module includes instructions to train the depth model including instructions to pre-train the depth model, the ray surface model, and a pose model according to a self-supervised training process that does not use the depth data as a ground truth comparison.
 7. The depth system of claim 1, wherein the depth model is a machine learning algorithm, and wherein generating the ray surface includes learning the camera type to provide the ray surface as part of the neural camera model that approximates the camera type for a set of training data including the pair of training images.
 8. A non-transitory computer-readable medium for semi-supervised training of a depth model using a neural camera model that is independent of a camera type and including instructions that when executed by one or more processors cause the one or more processors to: acquire training data including at least a pair of training images derived from a monocular video and depth data associated with at least one of the training images; train the depth model using the training data to generate a self-supervised loss from the pair of training images and a supervised loss from the depth data, wherein training the depth model includes learning the camera type by generating, using a ray surface model that is a neural network, a ray surface that approximates an image character of the training images as produced by a camera having the camera type and to create a synthesized image according to at least the ray surface and a depth map by i) lifting pixels to produce three-dimensional points using the ray surface, the depth map, and a camera center point and ii) projecting the three-dimensional points onto a context image to create the synthesized image; and provide the depth model to infer depths from monocular images in a device.
 9. The non-transitory computer-readable medium of claim 8, wherein the instructions to train the depth model include instructions to generate the supervised loss using a supervised loss function that compares values between the depth map and corresponding information from the depth data that is sparse Light Detection and Ranging (LiDAR) data, wherein the instructions to generate the supervised loss use the sparse LiDAR data to train the depth model on metric scale by accounting for scale aware differences between the depth map and the sparse LiDAR data and learns a camera center point associated with the ray surface.
 10. The non-transitory computer-readable medium of claim 8, wherein the instructions to train the depth model produce depth estimates according to a self-supervised structure from motion (SfM) process, and wherein the instructions to train the depth model include instructions to use the self-supervised loss and the supervised loss to update at least the depth model, a pose model, and the ray surface model.
 11. A method of semi-supervised training of a depth model using a neural camera model that is independent of a camera type, comprising: acquiring training data including at least a pair of training images derived from a monocular video and depth data associated with at least one of the training images; training the depth model using the training data to generate a self-supervised loss from the pair of training images and a supervised loss from the depth data, wherein training the depth model includes learning the camera type by generating, using a ray surface model that is a neural network, a ray surface that approximates an image character of the training images as produced by a camera having the camera type and to creating a synthesized image according to at least the ray surface and depth map by i) lifting pixels to produce three-dimensional points using the ray surface, the depth map, and a camera center point and ii) projecting the three-dimensional points onto a context image to create the synthesized image; and providing the depth model to infer depths from monocular images in a device.
 12. The method of claim 11, wherein training the depth model includes generating the supervised loss using a supervised loss function that compares values between the depth map and corresponding information from the depth data that is sparse Light Detection and Ranging (LiDAR) data, wherein generating the supervised loss using the sparse LiDAR data trains the depth model on metric scale by accounting for scale aware differences between the depth map and the sparse LiDAR data and learns a camera center point associated with the ray surface.
 13. The method of claim 11, wherein lifting the pixels includes scaling predicted ray vectors from the ray surface using the depth map and adjusting the predicted ray vectors according to the camera center point, and wherein projecting includes applying a softmax approximation to derive each pixel in the synthesized image by identifying a predicted ray vector from the ray surface that corresponds with a direction associated with the three-dimensional points as defined relative to the camera center point.
 14. The method of claim 11, wherein the image character associated with the camera type includes at least a format of the monocular images and lens distortion, and wherein the ray surface associates pixels within the monocular images with directions in an environment from which light that generates the pixels in the camera originates.
 15. The method of claim 11, wherein training the depth model to produce depth estimates is a semi-supervised process that integrates a self-supervised structure from motion (SfM) process, and wherein training the depth model includes using the self-supervised loss and the supervised loss to update at least the depth model, a pose model, and the ray surface model.
 16. The method of claim 11, wherein the self-supervised loss includes a photometric loss and a depth smoothness loss that separately account for pixel-level similarities, wherein training the depth model includes pretraining the depth model, the ray surface model, and a pose model according to a self-supervised training process that does not use the depth data.
 17. The method of claim 11, wherein the depth model is a machine learning algorithm, and wherein generating the ray surface includes learning the camera type to provide the ray surface as part of the neural camera model that approximates the camera type for a set of training data including the pair of training images. 